For this question, you may use the result ${{\left( \cos heta +\mathbf{i}\sin heta ight)}^{n}}

Question

For this question, you may use the result ${{\left( \cos \theta +\mathbf{i}\sin \theta \right)}^{n}}=(\cos n\theta +\mathbf{i}\sin n\theta )$.

Find the exact value(s) of $\theta $, where $-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}$, given that

${{\left( \cos \theta +\mathbf{i}\sin \theta \right)}^{3}}+{{(\cos \theta +\mathbf{i}\sin \theta )}^{5}}=-\frac{1}{2}-\frac{\sqrt{3}}{2}\mathbf{i}$.[6]

Accepted Answer

$\theta = \frac{\pi}{3}$

2022 DHS P1 Q4

2022 DHS P1 Q4

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